Open systems, i.e., systems that interact with their environment, undergo dephasing, decoherence and relaxaton. For systems that are coupled to Gaussian white noise, the stochastic dynamics can be described using the Schrödinger–Langevin equation [1]}. If one averages over the stochasticity, one can obtain a Markovian quantum master equation for the density matrix \(\rho (t)\)  with Lindblad operators \({\cal V}_j\)  [2]}, [1]}:
\( {\dot{\rho }} &=& -i [H(t), \rho (t)] \\ \nonumber &+& \frac{1}{2} \sum _j \xi _{0,j}^2\left(2{\cal V}_j \rho (t) {\cal V}^{\dag }_j - \rho (t) {\cal V}^{\dag }_j {\cal V}_j - {\cal V}^{\dag }_j {\cal V}_j \rho (t)\right) .\) 
